How do you bypass the security system?

The Chrysler Aspen uses the same security system as most Chryslers of that era and none of them have a way to bypass the security system that actually works. That is because they use multiple modules to operate and use the transponder to disable it. What is the issue you are having? There are a few common items that can cause it to stay armed or to randomly go off.

Basically I need to reprogram the key.

That isn't fun with Chrysler as you normally need a scan tool with security access to add or change keys because of the way the system works. You can only add new keys if you have 2 working keys. With none you have to use a scan tool or similar to erase and then add in the key.